J. Phys. Chem. 1993,97, 633-640
633
Oxygen on the Pd( 100) Surface: Desorption Dynamics with Surface Phase Transformations and Lateral Dipole Repulsions Kamil Klier,' Yam-Nan Wang, and Gary W. Simmons Zettlemoyer Center for Surface Studies and Department of Chemistry, b h i g h University. Bethlehem, Pennsylvania 18015 Received: May 14, I992
Phase transformations in oxygen overlayers on the Pd( 100) crystal face reported earlier (Simmons, G. W.; Wang, Y.-N.; Marcos, J.; Klier, K. J. Phys. Chem. 1991, 95, 4522) express themselves in a distinct and interesting kinetic behavior during oxygen desorption. The thermal desorption spectra (TDS) from the dense (e = 0.8) ( d 5 X d 5 ) R 2 7 O structure give rise to a sharp "explosivemdesorption peak demonstrating that a very high population of surface oxygen is nearly simultaneously activated for desorption; this is consistent with the proximity of fixed pairs of oxygen atoms in the ( d 5 X d 5 ) R 2 7 O structure proposed by Simmons et al. When this dense structure is partially depleted, a phase splitting occurs such that dense and rare (e = 0.4) phases coexist and desorption occurs from both until the dense phase is exhausted. The remainder of the rare phase obeys kinetic laws consistent with high mobility and strong lateral repulsion among the oxygen adatoms. Other phases of intermediate density such as ~ ( 2 x 2 (e ) = 0.50) or ~ ( 5 x 5 (e ) = 0.68) disproportionate into the dense ( d 5 X d 5 ) R 2 7 O structure and the rare phase only at temperatures just below desorption. A kinetic model that successfully describes the observed thermal desorption spectra involves a continuous equilibration of the dense and the rare phase during the desorption process. For the rare phase, both the King-Adams (King, D. A. Surf. Sci. 1975,47, 384. Adams, D. L. Surf. Sci. 1979,42,12) and the Klier-Zettlemoyer-Leidheiser-Devonshire (Klier, K.; Zettlemoyer, A. C.; Leidheiser, H. J. Chem. Phys. 1970,52, 589. Devonshire, A. F.Proc. R.SOC. London 1937,A163,132) models require lateral repulsion, 3.5 kcal/mol among nearest-neighbor occupied sites in the former and &/a3 in the latter (d = -2.85 D, a = distance between nearest-neighbor adatoms, variable with surface coverage), and both models reproduce the high-temperature TDS peak shifts and widths. However, the latter model accounts better for the high activation energy for desorption fromvery low coverages experimentally determined by a trailing edge analysis (-45-60 kcal/mol), large variation thereof with coverage, low value of activation energy a t initial coverages, and overall line shapes of the TDS peaks. In the dipole repulsion model, the transition state is a molecule with 0-0 distance 1.3 A, close to that of the gaseous oxygen molecule, that undergoes rotation and hindered translation in the array of oxygen adatoms.
Introduction In an earlier paper, we reported surface phase transformations that accompanied oxygen adsorption on the Pd( 100) crystal face as a function of surface coverage and temperature.' The results of these low-energy electron diffraction (LEED) and highresolution electron energy loss spectroscopy (HREELS) studies were reported and compared with those given in the literature for this system?+ We describe herein the observations of temperature desorption spectra (TDS) and LEED structures which show that the surface phases undergo dynamic interconversion while the desorption process is in progress. A kinetic model is presented that quantitatively accounts for the observed TDS patterns, including peak splitting from the initially homogeneous (dSXdS)R27O and ~ ( 2 x 2 structures. ) The parameters of the model are interpreted in terms of elementary interactions among the adatoms and the transition complex. The various surface phases of the oxygen/Pd( 100) system are summarized here to provide a basis for the description of the TDS patterns. For adsorption at room temperature, a wellorderedp(2X2) phase correspondingto 0.25 monolayer (ML) is formed after an oxygen exposure of 2 X lod Torr s (2 langmuirs or 2L) and a ~ ( 2 x 2phase ) corresponding to a saturation coverage of 0.50 ML is formed after 180-L exposure. To produce any further increase in oxygen adsorption, a surface temperature of 470 K was required at an oxygen pressure of 8.0 X lO-' Torr to form the ~ ( 5 x 5 structure, ) whereas the temperature had to be increased to 550 K to form the (d5XdS)R27O structure at this pressure.' Extended heating of thep(5X5) and (dSXdS)R27O structures under 8.0 X lO-' Torr of oxygen at 470 and 550 K, 0022-3654/58/2097-0633$04.00/0
respectively, produced neither changes in the structures nor increases in oxygen coverage, indicating that the fifth-order structures are equilibrium phases under these temperature and pressure conditions. The coverages for the ~ ( 5 x 5 )and (dSXdS)R27O structures were determined by Auger electron spectroscopy (AES) and TDS to be 0.68 and 0.80 ML, respectively.' Thec(2X2) phase,whichhadbeenformedatroomtemperature, undergoes an irreversible surface phase transformation at about 470 K in vacuum to a mixedp(SX5) and "(2x2)" phase without loss of oxygen to the gas phase.' A further irreversible phase transformation at 550 K in vacuum results in the formation of mixed (2x2) and (dSXd5)R27O phases. In fact, these transformations occur for all initial oxygen coverages greater than about 0.4 ML. A well-ordered ~ ( 5 x 5 )phase also changes irreversibly to a mixtureof the (2x2) and (dSXdS)R27O phases when heated to 550K in vacuum, whilea well-ordered ( 4 5 x 4 5 ) R27O structure does not undergo any phase transformation upon heating to 550 K. Heating the palladium crystal with initial coveragesgreaterthan 0.4 ML invacuum at temperatures between 550 and 650 K resulted in partial desorption of oxygen and the formation of mixed (dSXdS)R27O and (2x2) phases followed by the formation of a single (2x2) phase upon further loss of oxygen. It is particularly noteworthy that during the decomposition of the (dSXdS)R27O phase to (2x2) with partial desorptionof oxygen, neither thep(5X5) nor the 4 2 x 2 ) patterns were observed at room temperature for any of the intermediate coverages. Loss of oxygen from the (2x2) phase subsequently Q 1993 American Chemical Society
634 The Journal of Physical Chemistry, Vol. 97, No. 3, 1993 occurred at temperatures above 650 K and gave a clean Pd( 100) p ( 1X 1) structure. Molecular desorption from dilute atomic adsorbates requires surface mobility of the adatoms. At the same time, the present experimental data indicate strong lateral repulsion among the oxygen adatoms. Two models for this surface recombination with lateral repulsion are employed herein: (i) the King-Adams (KA) model,lOJ' which takes into consideration the coverage dependence of activation energy for desorption owing to adsorbate-adsorbate interactions and provides a statistical basis for the coverage dependenceof the frequency factor, and (ii) a model developed by Klier, Zettlemoyer, and Leidheiserl*based on a cell theory of wanderer molecules or adatoms in mobile adsorbates by DevonshireI3with addeddipole-dipolelateral repulsion (KZLD model). These models for the rare phase kinetic behavior are combinedwith that for thedesorptionfrom thedense ( 4 5 x 4 5 ) R27O phase, and the equilibration of the two phases during desorptionis taken into account. The models are compared with each other, and because of quantitative agreement of the KZLD model with experiment, the origin of lateral interactions is attributed to dipoledipole repulsions among Pdmeta16+O(af species.
Klier et ai.
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Experimental Section A descriptionof the experimental apparatus and experimental procedures used in this study was given earlier.' The crystal was circular, with the (100) surface 0.845 cmz and thickness 0.12 cm. During the TDS experiments, the crystal was positioned about 1 cm in front of the quadrupole mass spectrometer and heated at a rate of ca. 40 K/s. The mass spectrometer was controlled by a microcomputer, and several mass peaks could be monitored during thermal desorption. The mass peak intensities and the specimen temperature were recorded as a function of time. The temperature rise as a function of time was described by the following function: T/K = 298 75.56t - 1.878r2. Thermal desorption spectra were then presented in terms of mass peak intensity as a function of temperature. The ratioof the peak-to-peak Auger electron signalsfor oxygen (507 eV) and palladium (323 eV) was used as a measure of oxygen coverage along with the peak areas of the TDS. Both of these methods were calibrated assuming that the ~ ( 2 x 2and ) ~(2x2) LEED structures corresponded to coverages of 0.25 and 0.50 ML, respectively. Excellent agreement was found between the coverages determined by AES and TDS.'
+
ResultS The TDS patterns are presented as a function of oxygen coverage in Figure 1 . Oxygen was found to desorb as molecular oxygen for all coverages. At initial oxygen coveragesof less than 0.25 ML, a relatively broad and slightly asymmetric desorption peak was observed that shifted to lower temperatures with increasing initial coverage. This peak occurred at 850 K at a coverage of 0.02 ML and shifted to 760 K for a coverage of 0.25 ML. As the oxygen coverages became greater than 25 ML, this desorption peak first became more asymmetric and then a new and sharper peak located initially at 650 K emerged and grew in intensity, with the peak maximum occurring at 624 K at a coverageof 0.50 ML. The sharp peak increased in intensity with further increase in coverageup to the maximum coverageof 0.80 ML and shifted about 50 K to higher temperature. The results presented here are in general agreement with earlier studies for coverages to 0.506 and 0.60 ML.8,9 A partially resolved peak on the high-temperature side of the sharp thermal desorption peak, however, has been reported6v8sg but was not observed in the present study. This difference in thermal desorption behavior may be due to the higher heating rates used in our experiments. Details of the thermal desorption from coveragesgreater than 0.60 ML of oxygen on Pd( 100) surfaces have not been reported previously.
1
1
1
1
1
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I
Temperature, K
Figure 1. Thermal dcsorption spectra (TDS) of oxygen from the Pd-
(100) surface. Initial coverages 00 are, from bottom to top, 0.02,0.05, 0.11. 0.17, 0.25, 0.37, 0.43, 0.50, 0.68, and 0.80 in terms of Od/Pd,
atomic ratios. Theinitialroom-tempcraturestructuctures are markedp(2X2) for00 = 0.25,c(2X2)for 00 = O S O , p ( 5 X 5 ) for 00 = 0.68, and (d5xd5)R27O for eo = 0.80. The thermallyinduced surface phase transformationsdescribed earlier' were also observed during temperature-programmed desorption. Evidence for these transformations was obtained by interrupting the heating at specific temperatures, cooling the specimen to room temperature,and examining the LEED patterns. When the program temperature was interrupted just below the onset of desorption at 550 K from initial surface coverages of 0.40 ML I9 < 0.80 ML, mixed ~ ( 2 x 2and ) (dSXdS)R27* phases were observed at room temperature irrespective of the phase(s) originally present. Subsequent TDS patterns were the same as those obtained with uninterrupted experiments. The (dSXdS)R27O phase was stable upon heating to 550 K. When the heating was stopped at 660 K for any coverages greater than 0.35 ML and including the maximum coverageof 0.80 ML,after the sharp desorption at ca. 630 K had taken place, the ~ ( 2 x 2 ) residual oxygen phase was detected at room temperature. Subsequent thermal desorption from this residual ~ ( 2 x 2phase ) produced a TDS pattern identical to that obtained directly from the initial ~ ( 2 x 2phase. ) It is evident that the principalfeatures of the thermal desorption spectra, Le., the sharp low-temperature peak and the broad hightemperature peak, are associated with desorption from the (dSXdS)R27O phase and a rare phase that forms thep(2X2) structure at room temperature. The nature of the rare phase at the desorption temperatures is discussed below, based on models presented in Appendices I1 and 111. Since both TDS peaks were observed from an initial single (dSXt/S)R27O phase, it is apparent that the rare phase is a product of decomposition of the (dSXdS)R27O phase during partial desorption of oxygen. Integration of the thermal desorption spectra indicatedthat about 70% of the oxygen in the (dSXdS)R27O phase desorbs as the low-temperature peak and about 30%of the oxygen is converted to the rare phase at the temperature rise rates used. Oxygen in
The Journal of Physical Chemistry, Vol. 97, No. 3, 1993 635
Oxygen on the Pd( 100) Surface
Deaorptbn of O 2 from '(2x2Y 700
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Coverage, ML
1 . .
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Representation of adsorptionand thermal desorption with phase transformations from oxygen overlayers on Pd( 100). The dense ordered structure of (dSXd5)R27O is that proposed by Simmons et aleLThe "(2x2)" label refers to the disordered rare phase of variable density that is partially ordered at room temperature into a structure that displays ~ ( 2 x 2 )LEED spots at coverages less than 0.25 and ~ ( 2 x 2 )+ weak 4 2 x 2 ) spots at coverages 0.25-0.40.
the rare phase then desorbs as the higher temperature peak. Neither the 4 2 x 2 ) norp(5X5) initial phases participate directly in the desorption process since they undergo transformation to the mixed (d5Xd5)R27O and rare phases prior to the onset of oxygen loss.
Discussion Thekinetic behavior of the pure (d5Xd5)R27Ophase reflects the phase transformation occurring during desorption (Figure 1, Bo = 0.80 TDS curve): when this phase is partially depleted by the desorption process into a sharp TDS peak around 650 K,a new phase is formed that desorbs at higher temperature as a broad peak and upon cooling yields the ~ ( 2 x 2structure. ) The 4 2 x 2 ) hase, on the other hand, disproportionates into the ( d 5 X 5)R27" and the ~ ( 2 x 2phase ) before any desorption takes place, and then the desorption occurs from the mixed phase (d/5XdS)R27O and what becomes the ~ ( 2 x 2 phase ) upon cooling. This is in fact the case for all initial coverages 00 > 0.4, and therefore, only the dense (dSXd5)R27O and the rare phase coexist during desorption. At 00 < 0.4, a disordered ( 2 x 2 ) is formed upon cooling, and at these low coverages, desorptionoccurs only from the rare phase. A summary of this behavior is shown in Figure 2. In the dense phase, oxygen atoms do not have to travel a distancelarger than a few tenths of an angstrom to combine into an oxygen molecule, but in the rare phase, a considerable lateral movement of the adatoms is required for molecular desorption. Thus, any acceptable model for the rare phase must entail lateral mobility. The shifts of the rare-phase TDS peaks to higher temperatures with decreasing Bo reflect the biatomic desorption kinetics. However, the large widths of the hightemperaturepeaksalsoindicatelateralinteractionsoftheadatoms, and the shape skewed to lower temperatures suggests that these interactions are repulsive. The transition from the 2x2 phase to the disordered mobile phase that occurs below the desorption temperature is likely to remove the symmetric distortions of the Pd surface around the 4-fold sites evidenced by LEED.laZ1The energy associated with this transition is on the order of thermal energy at 550-600 K. Repulsive interactions in a pool of adatoms will be insignificant at near zero coverages and will assist desorption where the
9
Figure 3, Apparent activation energy for desorption, E., as a function of fractional monolayer (ML) coverage of oxygen on Pd(100). E, was determinedby the trailing edge analysisof TDS curvts for initial coveraga between 0.02 and 0.37, as shown in Appendix I. E, was determined from the slope of In (Ud/@) vs 1/T according to eq AI-3. The same analysis gives E. at the leading edge according to eq AI-4. Symbols refer to different Bo: ( 0 )(0.02,0.17), (*) 0.05. (v)O,ll, (v) 0.25, (0)0.31, (m) 0.37, (A) 0.43, (A) 0.50, ( 0 )0.68, ( 0 )0.80. The points forcoveragts between the trailing and the leading edge are included to indicate the validity of the limiting values of E. at low and high coverages.
adsorbatedensity is higher, giving rise to thedecreaseof activation energy for desorption with increased coverage. Such a behavior is confirmed by the results of the trailing edge analysis of the TDS curves (Appendix I) for the rare phase as demonstrated in Figure 3. The sharp decline of desorption energies with B at low coverages indicates that long-rangerepulsion forceso p t e . There is a wide range of desorption energies, 45-60 kcal/mol for nearzero coverage to less than 15 kcal/mol for coverages 0.2-0.3.The leading edge analysis14 of the TDS data of Figure 1, Bo = 0.25, yields thedesorptionenergiesin the range 20 5 kcal/mol, slightly higher than but in crude agreement with the values of Figure 3 for the coverages around 0.25 ML. The values of desorption energies in Figure 3 cover the entire range of literature data, either reported directly or calculated from the reported data by the authors. For coverages less than 0.05 ML, Milun et aLI5 report an activation energy for oxygen desorption of 52 kcal/mol for polycrystalline palladium using the leading edge analysis. For coverages between 0.05 and 0.1 ML, the activation energy dropped to about 39 kcal/mol. Chang and Thiel's- data for Pd(100) at coverages around 0.25 ML yield 10kcal/mol, in good agreement with our values of Figure 3 around 0.25 ML. The data of Stuve et a1.6 for oxygen desorption from Pd( 100) yield 55-60 kcal/mol for coverages 5 0.25 ML but the whole set of their TDS curves is at much higher temperatures (by 50-70 K) than those reported by Chang and Thiel and in the present work. We have carefully calibrated our temperature scale and believe the data in Figure 1are accurate. Other values have been reported, e.g., 55 kcal/molforPd( 111) at0.15 ML16bascdontheRedhead analysis of TDS maxima, the initial heat of oxygen adsorption on a reduced Pd powder, 49 kcal/mol,17 and 68 kcal/mol on evaporated Pd f i i l m ~ .The ~ ~ averagevalue of thedeaorptionenergy from the dense phase at initial coverages of 0.50,0.68, and 0.80 ML is, by the leading edge analysis, 49 kcal/mol, which is in a good agreement with the value of 49.7 kcal/mol reported by Chang and Thie18 and Chang et a1.9 for this range of coverages. To account for the desorption with phase transformation from the dense and rare structures quantitatively, we employed the models given in Appendices 11-IV. The equilibration between the two phases during desorption is described by the coupled
Klier et al.
636 The Journal of Physical Chemistry, Vol. 97, No. 3, 1993 differential equations (Appendix IV)
and
where Vd(8d) and vr(8,) are the desorption rates from the dense and rare phases with fractional coverages 8d and Or and each having nd and n, atoms per unit area, respectively. The rate Vd that successfully describes the sharp TDS peaks in all models is
+
where Ed = 41.3 8.1380 kcal/mol. The 80 dependence of E d was empirically determined from the positions of the maxima of the sharp TDS peaks in the range 00 = 0.80-0.50 ML. The rate vr was taken to be given by either eq AIII-I (the KA model) or eq A I M (the KZLD dipole repulsion model). Rates of adsorption into a precursor state and exchange rates of CO on nickel single crystals and their dependence on coverage were previously quantitatively accounted for by the KZLD theory.I2 In CO adsorbates, however,the surfacedipole is small, lateral interactions are dominated by the short-range Lennard-Jones potential, and no recombination of atoms takes place in molecular desorption. The KZLD model is now applied to atomic oxygen adsorbates with a large surface dipole and recombination of adatoms into a molecular transition state. The transition state in all models for desorption must be the sameas that for adsorption, and initial sticking probabilities provide a criterion for the nature of the activated complex: if the initial sticking probability (ao) is close tounityasin thechemisorptionofCOonNi(100) and Ni(1 1O),I2 no more than 1 translational degree of freedom is lost; if 1 rotational degree of freedom is lost, a0 drops to less than 0.1. The initial sticking probability of oxygen on Pd( 100) was reported to be 0.4.3 This lower than unity value can be attributed to the loss of degeneracy from 3 to 1when the gaseous triplet oxygen molecule is converted to the activated complex with concomitant electronic entropy change -R In 3 = -2.2 cal mol-' K-l corresponding to lowering of a0 byexp(&/R) = 0.33. Alternatively, lossofentropy due to hindrance of rotation could account for the initial a0 = 0.4. The entropy of 2.2 cal mol-l K-' was incorporated into the model for desorption. Each model was examined by fitting the TDS data of Figure 1by an optimization procedure,I9leaving as adjustable parameters the desorption energies at 8 = 0 for each of the two phases, the repulsion energy --o of the KA model, the Pdmeta++-O(af dipole repulsion energy D of the KZLD model, and the critical coverage Of below which the dense phase disappears (Appendix IV). After all the TDS spectra were subject to this procedure, the average valuesofEo,drEo,r,w,D,andO,wereused togeneratethe theoretical TDS curves for the two models. The two sets of theoretical simulated TDS spectra are shown in Figure 4a for the KA model and 4b for the KZLD model, with the values of the energy and repulsion parameters given in the legend. Both models required a critical coverage Oc = 0.40. Both models successfully reproduce the following features of the experimental TDS spectra of Figure 1: (i) the broad peak a t low initial coverage and its shift to lower temperatures with increasing coverage, (ii) the emergence of a narrow lowtemperature peak, and (iii) the relative areas under the narrow and broad peaks. This kind of agreement with experiment is strong evidence in support of the phase equilibration model. Each model shows minor departures from the observed line shapes of the high-temperature rare phase desorption peak: the KA model results in more symmetric and narrower TDS peaks than observed
300
600 900 Temperature, K
300
600 900 Temperature, K
F m e 4. Simulated TDS patterns for oxygen from Pd( 100) based on the dense phase-rare phase equilibrationmodel (Appendix IV)in which the rare phase is described by the following: (a) The King-Adam (KA) model (Appendix111) with the followingvalues of parameters: activation energy for desorption from the rare phase at zero coverage E,,, = 31.0 kcal/mol; activation entropy for desorption from the rare phase b r = -16 cal mol-' K-I; lateral repulsion energy in the rare phase -u = 3.5 kcal/mol; activation energy for desorption from the dense phase Ed = 41.3 kcal/mol + 8.1300kcal/mol; activationentropy for desorption from the dense phase A s d = 1 cal mol-' K-l; the critical coverage below which only the rare phase exists is 80 = 0.4. (b) The Klier-ZettlemoyerLeidheiser-Devonshire (KZLD) model (Appendix11) with the following values of parameters: activation energy for desorption from the rare phase at zero coverage E,, = 51.7 kcal/mol; dipole moment of the rare phase Pd,uld+O,& d = -2.85 D; activation energy for desorption from the dense phase Ed and 00 as in the KA model; activation entropica are calculated by the KZLD model for both phasea. For both the KA and the KZLD models, the critical coverage 8, = 0.4 above which the dense and the rare phase coexist and below which only the rare phase exists. Initial coverages in both sets of simulated spectra are, from bottom to top, 00 = 0.02,0.05,0.11,0.17,0.25,0.37,0.43,0.50,0.68, and0.80. The interpretation of the parameters of the simulatedspectra shown here and their comparison with the experimental spectra of Figure 1 are given in text.
and the KZLD model in longer than observed high-temperature tails produced from overlayers with 80 = 0.80 and 0.68 ML. The physical interpretation of the values of the various desorption energies and entropies obtained by the optimization process also involves fundamental similarities, as well as differences in the nature of the lateral motion of the adatoms, between the two models. In the KA model, the negative value found for the lateral interaction energy parameter ( w ) indicates repulsion between the oxygen adatoms. Similarly, in the KZLD model, the parallel dipole4ipole interaction is repulsive. The magnitude of the Pdmctald+-O(a)hdipole moment found using the KZLD model, d = -2.85 D, corresponds to the pairwise repulsion energy E d = &/a3 = 5.6 kcal/mol for the distance a = 2.15 A between neighboring oxygen atoms in the 4-fold holes. This is in an order of magnitude agreement with the repulsion --w = 3.5 kcal/mol found using the KA model. Further, the activation entropy for the rare phase, Asr = -16 cal mol-' K-I, required to place the TDS desorption peaks predicted by the KA model at the observed temperatures, indicates a large entropy stabilization of the adsorbate, which suggests that the adatoms have a large twodimensional mobility. In the KZLD scheme, the lateral mobility is an inherent part of the model via motion of oxygen atoms within the effective free area g (cf. Appendix 11). The activation energy for zero coverage, Eo,,= 31 kcal/mol, obtained from the
The Journal of Physical Chemistry, Vol. 97, No. 3, 1993 637
Oxygen on the Pd( 100) Surface
I
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-
_ I _
R O
r
4
R O
Figure 5. Representationof interactions of a moving dipole (center) at r with two dipoles at an average distance R determined by the adsorbate density. When the center dipole reaches the distance & from one of the other dipoles, molecular transition state 0 2 ' is formed and the two interacting dipoles vanish. The energy of the system is given by E = &[r3 R3 ( R - r)-3] where d is the magnitude of one dipole, and the activation energy for desorption E, = E(r = &) - E(r = R / 2 ) = &[&-' + ( R - &)" - 16R3].
+
+
KA model approachesthe average experimentalvalues(cf. Figure 3 ) . The KZLD model, however, finds Eqr = 5 1.7 kcal/mol and falls into the range of the initial activation energies for 8 0 obtained from the trailing edge analysis of experimental data. Due to the long-range nature of the dipole-dipole repulsion, a strong dependence of Er on coverage occurs even at small coverages. The dipole moment of -2.85 D corresponds to Pdmerat+O(afwhere 6 = 0.6 if the Pd-0 separation is 0.92-A normal to the surface? Taking the simple view that the Pdatom*+-O(afdipole is generated by the electronegativity difference between the oxygen and palladium atoms, 1.3,2O Pauling's correlation predicts ionic character 0.3, Le., 6 = 0.3 over the PdatOm-0distance. The equilibrium distance Pdatom-0 estimated from covalent radii is 2.06 A, and hence, the dipole moment is 2.97 D. Thus, the dipole moment estimated from the electronegativitydifference between oxygen and palladium atoms, -2.97 D, is close to that obtained from the present dipole repulsion model for the S P ( 1 0 0 ) TDS spectra, -2.85 D. The origin of activation energy for desorption is illustrated in Figure 5 , which schematicallydepicts the approach of two dipoles in the presence of another dipole. In the transition state, two adsorbate atoms meet at a critical distance Ro at which the molecular complex is formed and the dipolesvanish. This critical distance is expected to be of the order of interatomic distance in the diatomic molecule. The activation energy for desorption is then the difference between the dipole-dipole repulsion energy at Ro and R / 2 , Ea = ~ [ R o+-( R ~ - R0)-3- 2(R/2)-3]where R is determined by the coverage. For zero coverage, R and Ea(B-+O)= 8 / R 0 3 . From the KZLD model optimized for data of Figure 1, E,(-) = 51.7 kcal/mol and d = -2.85 D, which yields Ro = 1.3 A. This critical distance in the diatomic transition complex is indeed close to the interatomic distance in oxygen molecule, 1.2 A. With increasingadsorbatedensity 8, the average distance R between next nearest neighbors decreases and the activation energy for desorption becomes Ea(@= Ea(-) E ( R / 2 )as depicted in Figure 5 . The elementary model of Figure 5 illustrates the basic features of the dipole-dipole repulsion component of the model for an ensemble of many adatoms with
-
-
varying density described in Appendix 11. For dilute adsorbates, the dipole repulsion dominates over the Lennard-Jones shortrange potential, and the model is insensitive to large variations of the Lennard-Jones parameters A and SO*. We note that the dipole repulsion model developed here encompasses both the "through space" (electrostatic) and electronic (metal-oxygen bond polarization) interactionsin adsorbates and does not aim at distinguishing between the classical and the quantum mechanical picture. The surface dipole is obviously of quantum mechanical origin, and long-range interactions are treated as dominated by electrostatic interactions, as in many other chemical systems. The dipole repulsion may also affect the desorption energy from the dense (dSXdS)R27O structure, although the density of this structure remains constant during the desorption process and the dipole repulsion is a constant part of the desorption energy Ed (Appendix IV). One interesting aspect of the ( 4 5 x 4 5 ) R27O structure proposed by us earlier' is that the (Pd-O)-(Pd0)pairs at the shortest distances (but not at longer distances) are at an angle close to 90° at which dipole-dipole repulsion vanishes. Thus, for the dense structure, the dipole repulsion is reduced by an evasive tilting of the nearest dipoles. The dipole repulsion model also qualitatively predicts the behavior of oxygen adsorbate when a foreign electronegative adsorbate such as chlorineis introduced. The Pd-Cl dipole c a w oxygen desorption to occur at substantially lower temperatures than from the chlorine-free surface even at very low chlorine coverages.2' However, the present analysis shows that lateral repulsions are significant in the oxygen overlayer and the earlier employed Redhead analysis, which ignores lateral interactions, is inadequate for quantitative estimates of desorption energies. The experimentally observed shifts of the Pd-0 TDS peaks to lower temperatures due to surface chlorineindicate quite strongly that long-rangerepulsion phenomena control the oxygen coverages and thereby the availability of the mobile reactive oxygen for surface-catalyzed reactions. Summary nnd Conclusions
Oxygen desorption from overlayers on the Pd(100) crystal surface displays interesting surface phase transformations during the desorption process: the oxygen dense phase with atomic fraction density 0.8 continuously transforms into a rare mobile phase whenever the average surface density is less than 0.8, and desorptiontakes place from both phases in a competitive fashion. Successful quantitative models were developed for the desorption with phase transformation, as well as for the behavioir of the two phases separately. In the rare phase, the lateral interactions among oxygen adatoms are repulsiveand are effectiveover several Pd-Pd distances. In the KA model, the pairwise repulsion energy between the nearest-neighbor oxygen adatoms is comparable to that obtained from the KZLD dipole-dipole repulsion model corresponding to the polarity Pdmcm10.6+0~a~0.6. The difficulty of the KA model arises from the need to introduce a large negative activation entropy which is indicative of the adsorbate mobility in addition to the statistical entropy inherent in the model. This difficulty is overcome by employing the KZLD cell model of an array of mobile wanderer oxygen adatoms that suffer multiple repulsion interactions among the P d a + W dipoles, in which no empiricalentropy terms need to be introduced. While both modeln provide an adequate account for the main features of the TDS spectra in the range of initial coverages 80 = 0.024.80, the dipole repulsion model gives a better rationale for the high desorption energy at near-zero coveragesdetermined from experimentaldata by the trailing edge analysis. Also, the dipole repulsion model yields line shapes that very satisfactorily reproduce the experimental TDS curves. The dipole repulsion model also correctly predicts the behavior of oxygen adsorbates when a foreign electronegative adatom such as chlorine is introduced. The
638 The Journal of Physical Chemistry, Vol. 97, No. 3, 1993
Klier et al.
II: Theory of Desorption Rat- witb Lateral Dipole-Dipole Repulsion
consequenceis the weakening of the palladium-oxygen bond which may be a significant factor in catalyzed oxidation reactions.
Appendix
Appendix I: Tniling Edge Analysis of T e m p e n t u r e - P r o p d Desorption
Absolute rate theory in the form adapted by Klier et a1.I2for mobile adsorbates is used and modified further to describe recombinative desorption of atomic adsorbate to form diatomic gas, with lateral interactions due to a short-range Lennard-Jones potential and long-range dipole-dipole interactions.
This analysis aims at obtaining activation energies for desorption in the limit of low coverages. Assume second-order desorption kinetics, Yd
=@ exp(-E/kT)
where the frequency factorf dependson temperature and coverage 0 and the activation energy depends on coverage, E = E(8). The experiment is conducted so that 0 varies with temperature. Differentiation of (AI-1) with respect to /3 = (kT)-I yields
For f = c P , d In f/d/3 = -nkT and the contribution of the last term in (AI-2) to effective activation energy is of the order k T only. For small coveragesat the trailing edge of the temperatureprogrammed desorption experiment, the change of coverage is asymptotic with temperature and (de/dT) 0; hence,
-
[
]
d hl (vd/e2) lim dB = E(0) e-0
+ nkT
(AI-3)
and a slope of In ( U d / d 2 ) vs (kT)-I extrapolated to 0 0 gives the initial desorption energy E(0) with lateral interactions removed, except for a term on the order of thermal energy. If theactivation energyfor desorption varieslittle withcoverage, the term (dE/dB)(dO/dT) is small even for large variations of 0 with T, and the current trailing edge analysis is valid over a range of coverages 0. However, for large variations ,!?(e), the trailing edge analysis is limited to the lowest surface coverages. The implementation of the trailing edge analysis is illustrated in the diagram below. +
12
T1
-
[
lim e-0
dIn;/82)]
where A exp(N/kT) are the absolute activities of the activated complex (A*), the activated complex in its standard state (b’), and the surface atoms (b).The chemical potentials ~r, and bS aredetermined from the partition functionsof the adsorbedatoms and the activated complex which are derived from the model. f
The model for the adsorbate just prior to desorption is that of a mobile array of wanderer atoms (Yadatoms”)that carry dipoles d and interact laterally by the sum of pairwise potentials
4(r) = (A/r12)- (B/r6)+ (d2/r3)
(AII-2)
The activated complex is assumed to be the diatomic molecule on the surface that still ‘feels” the potential field of the adsorbate atoms except for the dipole interactions. Following Klier et aL12 and Devonshire,’) we use the adsorbate partition function for N, adatoms
N:l
2amkT 2 a s
= K7hi-)31,2
Nsx
and for the activated complex
Here the symbols have the following meaning: the pairwise intermolecular potential the Lennard-Jones potential constants
The shaded areas under the desorption curve (T2 to T = and T Ito T = m) are proportional to the coverages81 and 02 governing at temperatures TI and T2, from which the desorption rates Ud.1 and Ud.2 are measured. A plot of -[ln ( U d / e 2 ) ] vs 1/T has the initial slope equal to E(O)/k. It is noted that at the beginning of the thermal desorption where 0 00, the initial coverage, the change of coverage with temperature is also small, (dO/dT) 0, and we have for this ‘leading edge”
-
The rate of desorption is given by
(AI- 1)
= E(0,)
-
+ nkT
(AI-4)
where E(&) is the activation energy for desorption at the initial coverage which differs from E(0) at 0 0 of eq AI-3. In the case of significant lateral interactions, E(&,) of the leading edge is far from being indicative of activation energy at the TDS peak maxima or at near zero coverage.
the interaction constants according to Devonshir~~~ used in this work the distance between the centersof neighboring cells the average interaction energy for a wanderer m o l d e at a reduced squared distancey = (r/a)2 from the center of the cell the number of adatom adsorbed on an area s the number of activated complexes on an area s the effective occupied area the dipole moment of the adsorbate (may include an image dipole) in electrostatic unitsentimeter k Boltunann’s constant T absolute temperature the Madelung constant for the array of cella of the Md wanderer atom dipoles; the value 1.6 for a hexagonal array is taken from ref 12 lb)and m b ) are rational functions of y, defined by eq 9 in ref 13, and the integrals g, gl, and g,,, are defined in general as
Oxygen on the Pd( 100) Surface
The Journal of Physical Chemistry, Vol. 97, No. 3, 1993 639
The average interaction energy for a wanderer adatom with its dipole in a hexagonal two-dimensional cell is given by
The peripheral atoms contribute to the area by 3 atoms, and the density decreases locally from 5 adsorbate atoms on the left, S(SO/S),to 3 adsorbate atoms plus the activated molecule, 3(so/s) (so*/s), on the right. Thus,
+
e* = e(so**
+ 3So*)/(5So*)
and
= eP(so**+ ~s,*)s,**/(~s,*) S
where
SO*
+ 3 / 2 ) / r ( k + 1/2)12
nb)= r-'@[r(k
the remaining symbols having significance as above. The integral g* for the transition complex is analogous to g except that the dipole term 6(d2/a3)n(y) in +(y)is omitted because the transition complex is assumed to be neutral. The chemical potentials of the adsorbate atoms, b, and the activated complex, j ~ * are , given as
-= kT
(AII-4)
kT
and p* --
kT
f(3i)
kT-
[alnF*(T)
ax
I,
wheref(2i) andfoi) are the internal free energies of the adatoms and the molecular activated complex, respectively. As in ref 12, the absolute activity of the standard state b*is chosen such that N * / s = 1, and the desorption rate is determined as the number of molecules desorbed from unit area in unit time. The desorptionrate defined in (AII-1) becomes,using the chemical potentials of (AII-4),
(AIM)
while SO/S remains described by (AII-6). For oxygen on the Pd( 100) surface, p = 1.3223 X 10-15atoms/ cm2; the adsorbate areas SO* = 0.834 X lO-I5 c m 2 / 0 atom and SO** = 1.042 X cm2/02 complex are estimated from the Lennard-Jones constants of neon for oxygen atoms and those for gaseous oxygen molecule22reduced by 30% as in an earlier estimate of the adsorbed CO parameters.I2 Thus, for oxygen, eqs AIL6 and AII-8 give SO/S = 1.1038 and SO*/S = 1.1718. Similar estimates12v22 give the energy parameters A = 415 cal/mol and A* = 1351 cal/mol for the Lennard-Jones lateral interactions of the oxygen atoms and the activated molecular complex. For the dipole repulsion term N~Md362/a~, take d2 = p2/(4mo) where p is the dipole in C m (1 D = 3.33564 X C m) and 4m0 = 1.11265 X 1O-Io J-' C2 m-I . For a hexagonal cell array, the area per cell is ~ ~ 3 ~ /the ~ /coverage 2, 8 = (pa23l/2/2)-I, 0 - 3 = e3/2(p31/2/2)3/2, and the dipole repulsion energy N~Md362/a~ = LM3l2 where D = N~Md362(p3'/~/2)~/~. For example, for p = -2.85 D,Md = 1.6, and p = 1.3223 X loi9atoms/m2, D = 21.8 kcal/mol. The internal free-energy change, A f ( i ) - 2f@), is that associated with the change of internal degrees of freedom for 2 adsorbed atoms, 2f(2i),to the activated m~lecule,f(~~), Af(i) = A d i )- TAs('), where A d i ) = EOdenotes the internal desorption energy from infintely diluted adsorbate and Ad1>= s(3i)- 2d20 is taken to be the nontranslational entropy difference between the activated adsorbed molecule and two adsorbed atoms. Neglecting the vibrational entropy, As(')may be taken to be the entropy of the rotating molecule in its activated state and be approximated by the gas-phase rotational plus electronicentropyz3 s:i:iel= R In Zrot R T d In ZrOt/dT+R In w, Z,,= 8r2ZkTplp2/ (UP), where Z is the moment of inertia, plp2 is the nuclear spin entropy factor, u = 2 for homonuclear diatomic molecules, and w is the electronic degeneracy. For oxygen molecule, I = 19.47 X 10-4' kg m2, plp2 = 1 and w = 3 for its triplet state, and As~i~ie,(302) =1.38 +R In T i n (cal/mol)/K. If the activated complex is a singlet, As::$el = -0.803 R In T.
+
The surface concentrations SO/S = N,(so*/s) and SO*/S = NS(so**/s)are related to fractional coverages as follows:
-S = epso* SO
+
Appendix IIk King-Adam Model (AII-6)
(AII-7)
The Kinglo and Adams" model takes into consideration the coveragedependenceof the activationenergy owing to adsorbate adsorbate interactions and provides a statistical basis for the coverage dependence of the effective frequency factor. The form employed here entails the desorption rate expression
where p = NM~/S is the atom density of the metal per unit area, 8 is the fractional coverage of the adatoms, and 8* is an effective coverage of the activated complex in the pool of the adatoms. The value of 8' is estimated in terms of 8 from the model involving a site for two adsorbate atoms (diagram that follows, left) that react to form the activated molecule (diagram that follows, right) in the pocket of the nearest neighbors
where 8 is the fractional coverage, E, is the activation energy for desorption, E, = Eo + 2 4 1 - (1 - 28)/A], A = [ l - 48(1 e)( 1 - c/'T] 112, and w is the lateral interaction energy, o > 0 for lateral attraction and w C 0 for repulsion. The activation entropy As, is an empirical entity. If only internal degrees of
and
SO* = ~ * p s o * * S
640 The Journal of Physical Chemistry, Vol. 97, No. 3, 1993 freedom were involved in activation entropy, brwould be equal to b ~ ~ ~ ~aseinl Appendix ( 0 2 ) 11. Appendix IV Phase Equilibration Kinetic Model
Klier et al. yielding nd
= ed(n - e&/(ed -
"r
=
and
In this model, desorption occurs simultaneously from two surface phases which keep equilibrating during the desorption process. The dense phase (such as the Pd( 100) (dSXd5)R27O oxygen overlayer) has a constant density but keeps shrinking in size, while the rare phase has variabledensityand keeps increasing in size. In the model depicted below, and ns2are the numbers of metal atoms on a unit area available for the rare phase and dense phase, respectively, at the beginning of the desorption, G = - ~3 is the number of metal atoms covered by the dense phase during the desorption, and ~3 is the number of metal atoms available for the rare phase during desorption.
+
- n)/(ed -
(AIV-3)
The algorithm implementing the above relations entails the following steps: (i) For a given initial coverage 00, use eqs AIV-1 to calculate dnd and dnr in an interval dt at a time t from the governing m and n, (initially mo and nlo given by (AIV-2) and at time t by (AIV-3)). (ii) Calculate dn/dt = d(nd n,)/dt. (iii) Update m to nd - dm, nr to n, - dnrr and t to t dt. (iv) Repeat i-iii until dn/dt = 0. (v) If the temperature (Tj ramp in the TDS experiment was nonlinear, such as T = TO at l/*yt2,convert the time scale to the temperature scale. (vi) Plot -(dn/dt) vs temperature. The reaction rate expressions vr(er)for the desorptionfrom the rare phase that were alternatively used are obtained from the KZLD dipole repulsion model in Appendix I1 and the KA model in Appendix 111. The expression used for the rate Vd(8d) was
+ + +
+
where the activation entropy h d is the same as in the rare-phase models of Appendix I1 and Appendix 111 and the values of activation energy for desorption from thedense phasearedescribed in the text.
The numbers of adsorbate atoms in the dense and rare phase are m and n,, defining the adsorbate densities 8d = m/m and 8, = n,/(sl k3). The desorption rates from the dense and the rare phase are
+
dnd --= dt
n~4'd(8d)
and (AIV-I) where k4 = nd/& and k3 = 1 -a = 1 - m/8d. Equations AIV- 1 are coupled differential equations for m and n,. The total desorption rate is dn dnr dnd --=---dt dt dt and is determined from the following boundary conditions: at t = 0, m0 = &k2.Here n = n, + nd is the total coverage on unit area. Experiments show that there is a critical coverage0, below which only the rare phase can exist. Then initial concentration relations are
ndo =
-
-
n: =
-
-
and (AIV-2)
The present model further assumes that the dense and rare phases are in equilibrium at any time during thedesorptionprocess,
Acknowledgment. We acknowledge support from the U.S. Department of Energy, Basic Energy Sciences,and a grant from the AMOCO Corporation. References and Notes (1) Simmons,G. W.; Wang, Y.-N.;Marcos, J.;Klier, K.J.Phys. Chem. 1991, 95, 4522. (2) Reider, K. H.; Stocker, W. Surf. Sci. 1985, 150, L66. (3) Orent, T. W.; Bader, S. D. Surf. Sci. 1982, 115, 323. (4) Nyberg, C.; TengstA1, C. G. Solid State Comm. 1982, 44, 251. (5) Nyberg, C.; TengstAl, C. G. Surf. Sci. 1982,126, 163. (6) Stuve, E. M.;Madix, R. J.; Brundle, C. R. Surf. Sci. 1984,146,144. (7) Chang, S.-L.;Thiel, P. A. Phys. Reu. LLrr. 1987, 59, 296. f8) Chann. S.-L.:Thiel. P. A. J. Chem. Phvs. 1988. 88. 2071. (9j Chang; S.-L.; Thiel; P. A,; Evans, J. W: Surf. Ski. i988, 205, 117. (10) King, D. A. Surf. Sci. 1975, 47, 384. (1 1) Adam, D. L. Surf. Sci. 1974,42, 12. (12) Klier, K . ; Zettlemoyer, A. C.; Leidheiser, H. J. Chem. Phys. 1970, 52. 589. (13) Devonshire, A. F. Proc. R. Soc. London 1937, A163, 132. (14) Habenschaden,E.; Kiippers, J. Surf.Sci. 1984,138, L147. Vollmer, M.;Trager, F.Surf. Sci. 1987,187,445. Miller, J. B.;Siddiqui,H. R.;Gates, S.M.; Russel, J. N., Jr.; Yates, J. T., Jr.; Tully, J. C.;Cardillo, M.C. J. Chem. Phys. 1987.87, 6725. (15) Milun, M.;Pervan, P.; Wandelt, K . Sur. Sci. 1987,189/190,466. (16) Conrad, H.; Ertl, G.; Kiippers,J.; Latta, E. E. Surf. Sci. 1977,65, 245. (17) Bortner, M.H.; Parravano, G. Adv. Coral. 1957,9,424. (18) Brennan, D.; Hayward, D. D.; Trapnell, B. M. W. Proc. R. Soc. London 1960, A256. 8 1 . (19) The computer codes for the optimizationprocedureas well as for the calculationsusing models of Appendices 11-IV are availablefrom the authon. (20) Pauline, L. The Nature of the Chemical Bond, 3rd ed.; Come11 University Press: Ithaca, NY, 1991; pp 93 and 99. (21) Wang, Y.-N.; Marcos, J. A.; Simmons, G. W.; Klicr, K. J. Phys. Chem. 1990, 94.1591. (22) Hirschfelder,J. 0.;Curtiss, C. F.; Bird, R. B. Molecular Theory of Gases ondUquid; Wiley & Sons: New York, 1954; pp 1 1 10-1 1 1 1. Relations of the Hirschfelderet al. constants t and u and the presently used constants arc A 66 and SO* = [271/2/4]1/3a2. (23) Fast, J. D. Enrropy; McGraw-Hill: New York, 1962.
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